Search Results (44)

This study focuses on understanding the bioconvection in Jeffery–Hamel (JH) flow, which has valuable applications in areas like converging dies, hydrology, and the automotive industry, which make it a topic of practical importance. This research aims to explore Homogeneous–Heterogeneous (HH) chemical reactions in a magnetic Darcy–Forchheimer model with bioconvection in convergent/divergent channels. To analyze the role of porosity, the Darcy–Forchheimer law is applied. The main system of equations is simplified through similarity transformation into ordinary differential equations solved numerically with the help of the NDSolve technique. The results, compared with previous studies for validation, are presented through graphs and tables. The study reveals that in divergent channels, the velocity decreases with higher solid volume fractions, while in convergent channels, it increases. Furthermore, various physical parameters, such as the Eckert number and porosity parameter, increase skin friction in divergent channels but decrease it in convergent channels. These findings suggest that the parameters investigated in this study can effectively enhance homogeneous reactions, providing valuable insights for practical applications. Full article

Many aggregation operators are studied to deal with multi-criteria group decision-making problems. Whenever information has two aspects, intuitionistic fuzzy sets and Pythagorean fuzzy sets are employed to handle the information. However, q-rung orthopair fuzzy sets are more flexible and suitable because they cover information widely. The current paper primarily focuses on the multi-criteria group decision-making technique based on prioritization and two robust aggregation operators based on Aczel–Alsina t-norm and t-conorm. This paper suggests two new aggregation operators based on q-rung orthopair fuzzy information and Aczel–Alsina t-norm and t-conorm, respectively. Firstly, novel q-rung orthopair fuzzy prioritized Aczel–Alsina averaging and q-rung orthopair fuzzy prioritized Aczel–Alsina geometric operators are proposed, involving priority weights of the information. Several related results of the proposed aggregation operators are investigated to see their diversity. A multi-criteria group decision-making algorithm based on newly established aggregation operators is developed, and a comprehensive numerical example for the selection of the most suitable energy resource is carried out. The proposed aggregation operators are compared with other operators to see some advantages of the proposed work. The proposed aggregation operators have a wider range for handling information, with priority degrees, and are based on novel Aczel–Alsina t-norm and t-conorm. Full article

In multi-attribute group decision-making (MAGDM) problems, prioritization is sometimes important. Several techniques and methods have been introduced in fuzzy systems to use prioritization. The main purpose of this paper is to propose prioritized aggregation operators (AOs) for intuitionistic fuzzy (IF) information. These AOs are symmetric in nature and are based on the novel Aczel–Alsina t-norm and t-conorm. Herein, we propose IF-prioritized Aczel–Alsina averaging (IFPAAA) and IF-prioritized Aczel–Alsina geometric (IFPAAG) operators. It is shown that these AOs satisfy the basic features of aggregation. Some additional results for these AOs are also investigated. These proposed operators can capture the prioritization phenomenon among the aggregated arguments, and the weights for prioritization are obtained from expert information. Finally, the proposed AOs are used in an MAGDM problem where a doctor is selected for a hospital. A comparison of the proposed prioritized AOs is also established with other well-known AOs to show the significance of the IFPAAA and IFPAAG operators. Full article

Vendor management systems (VMSs) are web-based software packages that can be used to manage businesses. The performance of the VMSs can be assessed using multi-attribute decision-making (MADM) techniques under uncertain situations. This article aims to analyze and assess the performance of VMSs using MADM techniques, especially when the uncertainty is of complex nature. To achieve the goals, we aim to explore Hany mean (HM) operators in the environment of complex picture fuzzy (CPF) sets (CPFSs). We introduce CPF Hamy mean (CPFHM) and CPF weighted HM (CPFWHM) operators. Moreover, the reliability of the newly proposed HM operators is examined by taking into account the properties of idempotency, monotonicity, and boundedness. A case study of VMS is briefly discussed, and a comprehensive numerical example is carried out to assess VMSs using the MADM technique based on CPFHM operators. The sensitivity analysis and comprehensive comparative analysis of the proposed work are discussed to point out the significance of the newly established results. Full article

Using the strength of a single-valued neutrosophic set (SVNS) with the flexibility of a hesitant fuzzy set (HFS) yields a robust model named the single-valued neutrosophic hesitant fuzzy set (SVNHFS). Due to the ability to utilize three independent indexes (truthness, indeterminacy, and falsity), an SVNHFS is an efficient model for optimization and computational intelligence (CI) as well as an intelligent decision support system (IDSS). Taking advantage of the flexibility of operational parameters in Dombi’s t-norm and t-conorm operations, new aggregation operators (AOs) are proposed, which are named the SVN fuzzy Dombi weighted averaging (SVNHFDWA) operator, SVN hesitant fuzzy Dombi ordered weighted averaging (SVNHFDOWA) operator, SVN hesitant fuzzy Dombi hybrid averaging (SVNHFDHWA) operator, SVN hesitant fuzzy Dombi weighted geometric (SVNHFDWG) operator, SVN hesitant fuzzy Dombi ordered weighted geometric (SVNHFDOWG) operator as well as SVN hesitant fuzzy Dombi hybrid weighted geometric (SVNHFDHWG) operator. The efficiency of these AOs is investigated in order to determine the best option using SVN hesitant fuzzy numbers (SVNHFNs) in an IDSS. Additionally, a practical application of SVNHFDWA and SVNHFDWG is also presented to examine symmetrical analysis in the selection of wireless charging station for vehicles. Full article

The concept of m-polar spherical fuzzy sets (mPSFS) is a combination of m-polar fuzzy sets (mPFS) and spherical fuzzy sets (SFS). An mPSFS is an optimal strategy for addressing multipolarity and fuzziness in terms of ordered triples of positive membership grades (PMGs), negative membership grades (NMGs), and neutral grades (NGs). In this study, the innovative concept of m-polar spherical fuzzy topology (mPSF-topology) is proposed for data analysis and information aggregation. We look into the characteristics and results of mPSF-topology with the help of several examples. Topological structures on mPSFSs help with both the development of new artificial intelligence (AI) tools for different domain strategies and the study of different kinds of uncertainty in everyday life problems. These strategies make it possible to recognise and look into a situation early on, which helps professionals to reduce certain risks. In order to address various group decision-making issues in the m-polar spherical fuzzy domain, one suggestion has been to apply an extended linear assignment model (LAM) along with the SIR method known as superiority and inferiority ranking methodology in order to analyze road accident issues and dispute resolution. In addition, we examine the symmetry of optimal decision and perform a comparative study between the research carried out using the suggested methodology and several existing methods. Full article

This study considers the problem of selecting an anti-tank missile system (ATMS). The mentioned problem is solved by applying a hybrid multi-criteria decision-making model (MCDM) based on two methods: the DIBR (Defining Interrelationships Between Ranked criteria) and the MABAC (Multi-Attributive Border Approximation area Comparison) methods. The methods are modified by applying rough numbers, which present a very suitable area for considering uncertainty following decision-making processes. The DIBR method is a young method with a simple mathematical apparatus which is based on defining the relation between ranked criteria, that is, adjacent criteria, reducing the number of comparisons. This method defines weight coefficients of criteria, based on the opinion of experts. The MABAC method is used to select the best alternative from the set of the offered ones, based on the distance of the criteria function of every observed alternative from the border approximate area. The paper has two main innovations. With the presented decision-making support model, the ATMS selection problem is raised to a higher level, which is based on a proven mathematical apparatus. In terms of methodology, the main innovation is successful application of the rough DIBR method, which has not been treated in this way in the literature so far. Additionally, an analysis of the literature related to the research problem as well as to the methods used is carried out. After the application of the model, the sensitivity analysis of the output results of the presented model to the change of the weight coefficients of criteria is performed, as well as the comparison of the results of the presented model with other methods. Finally, the proposed model is concluded to be stable and multi-criteria decision-making methods can be a reliable tool to help decision makers in the selection process. The presented model has the potential of being applied in other case studies as it has proven to be a good means for considering uncertainty. Full article

The Fermatean fuzzy set (FFS) is a momentous generalization of a intuitionistic fuzzy set and a Pythagorean fuzzy set that can more accurately portray the complex vague information of elements and has stronger expert flexibility during decision analysis. The Combined Compromise Solution (CoCoSo) approach is a powerful decision-making technique to choose the ideal objective by fusing three aggregation strategies. In this paper, an integrated, multi-criteria group-decision-making (MCGDM) approach based on CoCoSo and FFS is used to assess green suppliers. To begin, several innovative operations of Fermatean fuzzy numbers based on Schweizer–Sklar norms are presented, and four aggregation operators utilizing the proposed operations are also developed. Several worthwhile properties of the advanced operations and operators are explored in detail. Next, a new Fermatean fuzzy entropy measure is propounded to determine the combined weight of criteria, in which the subjective and objective weights are computed by an improved best-and-worst method (BWM) and entropy weight approach, respectively. Furthermore, MCGDM based on CoCoSo and BWM-Entropy is brought forward and employed to sort diverse green suppliers. Lastly, the usefulness and effectiveness of the presented methodology is validated by comparison, and the stability of the developed MCGDM approach is shown by sensitivity analysis. The results shows that the introduced method is more stable during ranking of green suppliers, and the comparative results expound that the proposed method has higher universality and credibility than prior Fermatean fuzzy approaches. Full article

Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of $\left[0, 1\right]$. The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established. Full article

The idea of spherical fuzzy soft set (SFSS) is a new hybrid model of a soft set (SS) and spherical fuzzy set (SFS). An SFSS is a new approach for information analysis and information fusion, and fuzzy modeling. We define the concepts of spherical-fuzzy-soft-set topology (SFSS-topology) and spherical-fuzzy-soft-set separation axioms. Several characteristics of SFSS-topology are investigated and related results are derived. We developed an extended choice value method (CVM) and the AHP-TOPSIS (analytical hierarchy process and technique for the order preference by similarity to ideal solution) for SFSSs, and presented their applications in multiple-criteria group decision making (MCGDM). Moreover, an application of the CVM is presented in a stock market investment problem and another application of the AHP-TOPSIS is presented for an environmental mitigation system. The suggested methods are efficiently applied to investigate MCGDM through case studies. Full article

We introduce the notion of the interval-valued linear Diophantine fuzzy set, which is a generalized fuzzy model for providing more accurate information, particularly in emergency decision-making, with the help of intervals of membership grades and non-membership grades, as well as reference parameters that provide freedom to the decision makers to analyze multiple objects and alternatives in the universe. The accuracy of interval-valued linear Diophantine fuzzy numbers is analyzed using Frank operations. We first extend the Frank t-conorm and t-norm (FT${}_c$T${}_n$) to interval-valued linear Diophantine fuzzy information and then offer new operations such as the Frank product, Frank sum, Frank exponentiation, and Frank scalar multiplication. Based on these operations, we develop novel interval-valued linear Diophantine fuzzy aggregation operators (AOs), including the “interval-valued linear Diophantine fuzzy Frank weighted averaging operator and the interval-valued linear Diophantine fuzzy Frank weighted geometric operator”. We also demonstrate various features of these AOs and examine the interactions between the proposed AOs. FT${}_c$T${}_n$s offer two significant advantages. Firstly, they function in the same way as algebraic, Einstein, and Hamacher t-conorms and t-norms. Secondly, they have an additional parameter that results in a more dynamic and reliable aggregation process, making them more effective than other general t-conorm and t-norm approaches. Furthermore, we use these operators to design a method for dealing with multi-criteria decision-making with IVLDFNs. Finally, a numerical case study of the novel carnivorous issue is shown as an application for emergency decision-making based on the proposed AOs. The purpose of this numerical example is to demonstrate the practicality and viability of the provided AOs. Full article

Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding data is not generally symmetric on the grounds that it does not provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due to their parameter variableness, they have been well applied in MADM under fuzzy construction. Recently, the Aczel-Alsina AOs on intuitionistic fuzzy sets (IFSs), interval-valued IFSs and T-spherical fuzzy sets have been proposed in the literature. In this article, we develop new types of Pythagorean fuzzy AOs by using Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Thus, we give these new operations Aczel-Alsina sum and Aczel-Alsina product on Pythagorean fuzzy sets based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. We also develop new types of Pythagorean fuzzy AOs including Pythagorean fuzzy Aczel-Alsina weighted averaging and Pythagorean fuzzy Aczel-Alsina weighted geometric operators. We elaborate some characteristics of these proposed Aczel-Alsina AOs on Pythagorean fuzzy sets, such as idempotency, monotonicity, and boundedness. By utilizing the proposed works, we solve an example of MADM in the information of the multinational company under the evaluation of impacts in MADM. We also illustrate the comparisons of the proposed works with previously existing AOs in different fuzzy environments. These comparison results demonstrate the effectiveness of the proposed Aczel-Alsina AOs on Pythagorean fuzzy sets. Full article

In today’s world, the countries that have easy access to energy resources are economically strong, and thus, maintaining a better geopolitical position is important. Petroleum products such as gas and oil are currently the leading energy resources. Due to their excessive worth, the petroleum industries face many risks and security threats. Observing the nature of such problems, it is asserted that the complex bipolar fuzzy information is a better choice for modeling them. Keeping the said problem in mind, this article introduces the novel structure of complex bipolar fuzzy relation (CBFR), which is basically used to find out the relationships between complex bipolar fuzzy sets (CBFSs). Similarly, the types of CBFRs are also defined, which is helpful during the process of analyzing and interpreting the problem. Moreover, some useful results and interesting properties of the proposed structures are deliberated. Further, a new modeling technique based on the proposed structures is initiated, which is used to investigate the security risks to petroleum industries. Furthermore, a detailed comparative analysis proves the advantages and supremacy of CBFRs over other structures. Therefore, the results achieved by the proposed methods are substantially reliable, practical and complete. Full article

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. Multi-attribute decision-making (MADM) technique is a very effective and well-known tool to investigate fuzzy information more effectively. However, the selection of houses cannot be carried out by utilizing symmetry information, because enterprises does not have complete information, so asymmetric information should be used when selecting enterprises. Hamy mean (HM) operator is a feasible tool to handle strategic decision-making problems because it can capture the order between the finite input terms. Additionally, the complex interval-valued q-rung orthopair fuzzy (CIVq-ROF) setting is a broadly flexible and massively dominant technique to operate problematic and awkward data in actual life problems. The major contribution of this analysis is how to aggregate the collection of alternatives into a singleton set, for this we analyzed the technique of CIVq-ROF Hamy mean (CIVq-ROFHM) operator and CIVq-ROF weighted Hamy mean (Cq-ROFWHM) operator and some well-known results are deliberated. Keeping the advantages of the parameters in HM operators, we discussed the specific cases of the invented operators. To investigate the decision-making problems based on CIVq-ROF information, we suggested the following multi-attribute decision-making (MADM) technique to determine the beneficial term from the finite group of alternatives with the help of evaluating several examples. This manuscript showed how to make decisions when there is asymmetric information about enterprises. Finally, based on the evaluating examples, we try to discover the sensitive analysis and supremacy of the invented operators to find the flexibility and dominancy of the diagnosed approaches. Full article

T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited room for processing such kinds of information. On a scale of zero to one, similarity measures (SMs) are a tool for evaluating the degrees of resemblance between various items or phenomena. The goal of this paper is to investigate the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment. The newly improved SM has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss. The proposed SM’s validity is demonstrated mathematically and by examples. To examine the application of the suggested SM two real-life issues are discussed, including the concerns of medical diagnosis and pattern recognition. A comparison of the suggested SMs with current SMs is also made to assess the proposed work’s reliability. Since symmetric triangular fuzzy numbers are quite useful in database acquisition, we will consider the proposed SM for symmetric T-spherical triangular fuzzy numbers in the near future. Full article